Acoustic measurement method and apparatus

ABSTRACT

Method and apparatus for simultaneous acoustic measurement at a point (M) in space of the three components of the sound intensity vector. A preferred omnidirectional vector probe ( 40 ) includes a central ring ( 42 ) with four small, microphones on tubes attached to the ring spaced from one another in a regular tetrahedral arrangement. The tubes are parallel to the axis of the ring, two on one side ( 58 ) and two on the reverse side ( 60 ) of the ring, with two of the microphones pointing in one direction and two in the opposite direction. The microphone signals are processed by an analog-to-digital converter feeding a digital signal processor ( 68 ) and employing a cross-spectral formulation to compute a sound intensity vector at the measurement point (M). Sound velocity and pressure can also be determined at this point. The resulting data may be outputted on a computer screen or other device ( 70 ). Additional related features and methods are disclosed.

TECHNICAL FIELD

This invention relates to the measurement of the sound-intensity vectorand, more particularly, to methods and means of performing suchmeasurement with four small microphones.

BACKGROUND OF THE INVENTION

Previous Attempts to Measure the Sound-Intensity Vector

The sound-intensity vector, or sound power flow per unit area, isdefined as the product of sound pressure and sound velocity. It isdifficult to measure as a function of time and is usually determined asa function of frequency. Ways of measuring sound intensity are describedin

-   1. F. J. Fahy, 1995, “Sound Intensity”, Second Edition, E& FN Spon,    An imprint of Chapman and Hall, London.-   2. Anon., 1996, “Instruments for Measurement of Sound Intensity”,    Standard ANSI S1.9-1996, American National Standards Inst.    Sound intensity is not measured directly. It involves the use of a    measurement calculation. Generally only one component of the    intensity vector is measured using a pair of microphones.    Two-microphone instruments are discussed almost exclusively by Fahy    and in the ANSI standard, except that on pages 112 and 113 of Fahy    two instruments are described that measure all three components of    the intensity vector using four or more microphones.

The first of these instruments uses a probe consisting of three pairs ofcondenser microphones aligned face-to-face along three Cartesian axes. Aprobe of this type is manufactured, for example, by GRAS Sound &Vibration ApS in Denmark, as model number 50VI, and is described in

-   3. P. Rasmussen, 1989, “Source Location using Vector Intensity    Measurements”, Sound and Vibration Magazine, Vol. 23, pages 28–33.    Each pair of microphones is phase matched to provide better accuracy    at low frequencies. Six microphones are used because it is easier to    select phase matched condenser microphones in pairs, during    manufacture. However six is more than is necessary, making the probe    particularly unwieldy. A requirement for accuracy in the measurement    calculation is that the sensitivity of the probe is omnidirectional;    i.e. is equally sensitive to sound from all directions. However,    because the six microphones have manufacturing variability and do    not respond identically, the sensitivity of the GRAS probe is not    omnidirectional. The usual calibration in the field at a single    frequency cannot correct for this. Also the structure of the    six-microphone probe prevents it from making measurements close to a    source. Two sizes (typically 12 and 50 mm) of solid spacers are used    to separate the faces of the three pairs of microphones in the    probe. The smaller spacer is used for accuracy at higher frequencies    and the larger for accuracy at lower frequencies. This means that    the probe can not make accurate measurements at the same measurement    point, concurrently at both low and high frequencies. Although it    would be possible to output data on sound pressure and velocity with    this instrument, no attempt was made to do this. Also    azimuth-elevation plots were not used by P. Rasmussen to represent    the direction of a sound source.

The second instrument for measuring the three components of soundintensity cited by Fahy was manufactured by Ono Sokki in Japan as modelMI-6420. It uses a probe consisting of four condenser microphonespositioned at the vertices of an imaginary regular tetrahedron. Thetetrahedral arrangement is well known. Originally it appears to havebeen mentioned by

-   4. G. Rasmussen, 1985, “Measurement of Vector Fields”, pages 52–58,    Proc. Second International Congress on Acoustic Intensity, CETIM,    Senlis, France.    and discussed later by-   5. L. M. C. Santos, C. C. Rodrigues and J. L. Bento-Coelho, 1989,    “Measuring the Three Dimensional Acoustic Intensity Vector with a    Four-Microphone Probe”, Proceedings of INTER-NOISE 89, 965–968.    A regular tetrahedron has the basic geometric property that lines    joining the midpoints of opposite edges form a set of Cartesian    axes, thus providing a ready-made coordinate system for determining    the components of the sound intensity vector, with the measurement    point at the origin. This property is used by the Rasmussens and by    Santos et al, but surprisingly it was not used in the Ono-Sokki    instrument. Instead one of the coordinate axes is assumed to pass    through a microphone that protrudes ahead of the other three, as    described by-   6. H. Suzuki, “Three dimensional acoustic intensity measuring    device”, Japanese Patent No. 0528898, Nov. 2, 1993.    This coordinate system appears to have been used first by-   7. K. Segiguchi, S. Kimura and T. Hanyuu, 1992, “Analysis of Sound    Field on Spatial Information using a Four-Channel Microphone System    on Regular Tetrahedron Peak Point Method”, Applied Acoustics, 37,    305–323.    In this latter paper the direction of a sound source is determined    using time of flight, rather than from the direction of the    sound-intensity vector. An account of the measurement calculation    for the Ono-Sokki instrument is given in-   8. H. Suzuki, S. Oguro, M. Anzi and T. Ono, 1995, “Performance    evaluation of a three dimensional intensity probe”, Journal. of the    Acoustical Society of Japan, (E), 16, 4, pages 232–238.    Because of the singular nature of the coordinate system, the    calculation is complicated and subject to error. Even though the    Suzuki probe uses fewer microphones than the GRAS probe it is still    somewhat unwieldy and cannot detect sound well from the direction of    the microphone preamplifiers and leads. As with the GRAS instrument,    the microphones in the probe do not respond identically, so that the    sensitivity of the probe is not omnidirectional. Also the instrument    cannot make accurate measurements concurrently at both low and high    frequencies. No attempt is made to present data on sound pressure    and sound velocity. Also the Ono-Sokki and the Segiguchi instruments    do not use practical azimuth-elevation plots to indicate the    direction of a sound source.    Condenser and Electret Microphones

The GRAS, Ono-Sokki and Segiguchi instruments all use condensermicrophones. A condenser microphone is generally made with a stainlesssteel membrane and other metal parts. It is very stable, making itsuitable for use as a standard. However, it requires a pre-amplifier,usually contained in a metal tube, which has to be included as part ofthe structure of the probe Condenser microphones are relatively large.The microphones in the GRAS and Ono-Sokki systems are about 12.7 and 7mm in diameter. The center of sensitivity of a microphone can not beassumed to be the geometric center of the membrane. Hence, for largermicrophones, it is not possible to make an accurate determination of theinter-microphone spacing in the probe. This spacing has to be knownaccurately for best accuracy in the measurement calculation. As shownlater, the problem of locating the center of sensitivity of a microphoneis greatly alleviated with small microphones that use a thin film ofpolarized material called an electret

Measurement Calculation

Sound intensity is generally determined using the cross-spectralformulation, first derived in 1977 (see Fahy) for a two-microphoneprobe. This formulation relates sound intensity to the cross spectrum ofthe sound pressures at the microphones. It was discussed by

-   9. J. Y. Chung, “Sound Intensity Meter”, U.S. Pat. No. 4,236,040,    Nov. 25, 1980.    The formulation uses finite-difference approximations based on the    requirement that the microphone spacing is less than the wavelength    of the sound being measured. This requirement places an upper limit    on the frequency range of the measurement. A three-dimensional    version of the cross-spectral formulation was used by-   10. R. Hickling and W. Wei, 2000, “Use of pitch-azimuth plots in    determining the direction of a noise source in water with a vector    sound-intensity probe”, Journ. Acoust. Soc Amer, 97(2), pp 856–866.    In this paper the probe consists of four hydrophones in the    tetrahedral arrangement. Since the hydrophones do not have the same    frequency response, the sensitivity of the probe is not    omnidirectional. Also the hydrophone spacing is not known precisely    so that the measurement calculation is correspondingly less accurate    and the measurement point is not known precisely. Hickling et al    employ azimuth-elevation plots to represent the direction of a sound    source. Other types of representation are used by P. Rasmussen and    by Segiguchi et al.

BACKGROUND OF THE INVENTION—OBJECTS AND ADVANTAGES

The recent availability of small, sensitive electret microphones hasmade possible a practical and precise apparatus and procedure formeasuring the three components of the sound intensity vector. The probeuses four microphones in the tetrahedral arrangement. The instrument canbe used by technicians with normal computer skills and requires noin-depth acoustical training. What is needed and desired is:

-   -   (a) a probe that is easily handled    -   (b) a probe where the inter-microphone spacing is known        accurately    -   (c) a means of normalizing and calibrating the microphones to        make the probe omnidirectional    -   (d) a probe where the position of the measurement point is known        accurately.    -   (e) a means of measuring sound intensity at a single point over        a broad frequency range.    -   (f) a probe that is inexpensive    -   (g) mathematically efficient methods of measurement calculation        that can be readily incorporated into a digital signal        processor.    -   (h) a system where the direction of a sound source is        represented in a practical and useful manner.    -   (i) a system that provides ancillary sound-velocity and        sound-pressure data in addition to sound-intensity data.        Further objects and advantages of this invention will become        apparent from a consideration of the following description and        drawings.

SUMMARY OF THE INVENTION

The present invention includes and utilizes an instrument and method,which simultaneously measures the three components of thesound-intensity vector. The instrument includes a probe withomnidirectional sensitivity (to be explained), consisting of four smallmicrophones positioned at the vertices of an imaginary regulartetrahedron. The probe is linked to a digital signal processor thatcalculates the three components of the sound-intensity vector, using thecross-spectral formulation (to be described later) based onfinite-difference approximations (to be explained), and presents theresults on a computer monitor or other output device.

A major factor in the invention is the recent availability of smallelectret microphones, which provides much greater flexibility in designof the structure of the probe and facilitates many of the improvementsdescribed here. Instead of a preamplifier, these microphones have a verysmall JFET (Junction Field Effect Transistor) within the microphone.Examples of small electret microphones are the FG series from KnowlesElectronics LLC, of Ithaca Ill., which have a diameter of about 2.6 mm,and the EM series of Primo Microphones Inc., of McKinney, Tex., whichhave a diameter of about 5.8 mm. Because of their small size the centerof sensitivity and inter-microphone spacing of electret microphones canbe determined more precisely. This makes the measurement calculationmore accurate. The Knowles FG series microphones have a sensitivitycomparable to much larger condenser microphones, which makes themparticularly suited to this invention. An important additional factor isthat electret microphones are much cheaper than condenser microphones.Also the leads are much narrower. Their only drawback appears to be thatthey are less stable. However this can be compensated for by thenormalization and calibration procedure described here. Smallmicrophones can be positioned more closely, permitting measurements tobe made at higher frequencies.

In the probe, use is made of the geometric property of a regulartetrahedron where the lines joining the mid-points of opposite edgespass through a central point, forming a set of Cartesian axes.Measurements are made at the origin, i.e. the geometric center of thetetrahedron The axes determine the direction of the vector components ofsound intensity.

A feature of the invention is that the probe includes a small compactsupport structure for the microphones, that may have a ring of diameterd with four microphones in tubes attached to the ring, two tubespointing in one direction parallel to the axis of the ring and twopointing in the opposite direction on the reverse side of the ring. Eachpair of microphones lies in a plane on diametrically opposite sides of acircumference, the pair on one side being rotated ninety degreesrelative to the pair on the other side, one pair being a distanced/√{square root over (2)} from the other. The center of the ring is themeasurement point. The distance d is such that it is smaller than theshortest wavelength of sound being measured.

Measurement accuracy is ensured by a novel normalization and calibrationprocedure to make the sensitivity of the probe omnidirectional by makingthe frequency responses of the four microphones appear identical in thesignal processor. The procedure also makes the signals from themicrophones in the probe more accurate.

Also, in accordance with another aspect of the invention, it is possibleto perform accurate measurements over a broader frequency range thanbefore, with a nested set of two or more tetrahedral arrangements withdifferent spacing d, having the same orientation and measurement point.

Yet another feature is that the sound-intensity vector provides acompact and accurate way of determining the direction of a sound sourcein air. This can be displayed on a monitor screen in the form of aneasily understood elevation-azimuth plot or other suitablerepresentation. Elevation-azimuth plots were used by Hickling et al.Other representations were used by Segiguchi et al and by P. Rasmussen.The practicality of the elevation-azimuth representation can bedemonstrated by a suitable holder for the sound-intensity probe. Withthis holder the elevation and azimuth of the probe can be adjustedeither by hand or by remote digital control, so that it points at asound source. Direction can then be indicated by laser pointers attachedto the holder. Finding the direction to a noise source at a knownlocation is the only way of checking the accuracy of the sound-intensityvector.

Another feature of the holder is that the narrow leads from the fourmicrophones are routed so as to reduce interference with the soundfield, thus helping to preserve the ommidirectional nature of the probe.This can be accomplished, by laying a lead along a radial spoke of theholder and thence around the outer frame to the handle and the digitalsignal processor. The handle of the holder can contain batteries for thelaser pointers.

Yet another feature is that the measurement system provides ancillarydata on the other two basic quantities of acoustics, namely soundvelocity and sound pressure.

Although there are a number of facets to this invention, it has a singlepurpose, namely to provide a practical, accurate and inexpensiveinstrument and method for measuring the sound-intensity vector.

These and other features and advantages of the invention will be morefully understood from the following description of certain specificembodiments of the invention taken together with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is a block schematic diagram illustrating the vector probe,digital signal processor and other apparatus utilized in carrying outthe method of the present invention.

FIG. 2 is a cubic lattice diagram showing the geometry of thetetrahedral arrangement of microphones and the relation of themicrophones to a system of Cartesian coordinates with the origin M wheremeasurements are made.

FIG. 3 is a perspective view of an acoustic vector probe forming a partof the invention.

FIG. 4 is a side view of the probe of FIG. 3.

FIG. 5 is a plan view of the probe in FIG. 3

FIG. 6 is a side view of a calibration apparatus for normalizing andcalibrating the microphones in the vector probe.

FIG. 7 is a side view of a fixture applied to the vector probe for usewith the calibration apparatus, and positioned for assembly into thecalibration apparatus, for normalizing and calibrating the two pairs ofmicrophones, one pair on each side of the ring of the vector probe.

FIG. 8 is a plan view of a nested pair of vector probes with the sameorientation and measurement point for extending the frequency range ofthe measurement.

FIG. 9 is a side view of a nested pair of vector probes with the sameorientation and measurement point.

FIG. 10 shows the coordinate system for determining the direction of asound-intensity vector in azimuth and elevation, relative to theorientation of a vector probe.

FIG. 11 shows a holder for a vector probe that can be adjusted inazimuth and elevation, with spokes spreading radially from eachmicrophone, the direction of a sound source being indicated by smalllaser pointers in the holder.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 is a block diagram illustrating the acoustic measurementapparatus of the present invention. Block 40 represents the vector probe40 carrying microphones 1, 2, 3 and 4. The four microphones areconnected to a converter 66 that converts the analog signals from themicrophones to digital form for input to a digital signal processor 68.The processor normalizes the digitized signals using transfer functionsdetermined using a novel technique to be described later. At themeasurement point, it computes the three components of thesound-intensity vector and, additionally, the three components of thesound-velocity vector and the sound pressure, using mathematicalrelations to be subsequently discussed, and presents the results on amonitor screen or other output device indicated by numeral 70. Theinvention uses a cross-spectral formulation, to be subsequentlydescribed, to determine sound intensity. The signal processor can alsodetermine the direction of a sound source from the components of thesound intensity vector by a method to be described, presenting theresults on the monitor screen or other device 70. The signal processorcould have eight or more input channels corresponding to two or morenested acoustic vector probes, as shown in FIGS. 8 and 9. For the firsttime in such an application, the invention uses very small electretmicrophones. The vector probe 40 is compact and inexpensive. It can beused in applications such as noise control and architectural acoustics.

In FIG. 2, the geometric placement of the microphones in the tetrahedralarrangement is shown inserted within a cubic lattice 64 having 6 faceswith midpoints 12, 13, 14, 23, 24, 34. Microphones 1 through 4 arelocated at the vertices of an imaginary regular tetrahedron. Linesthrough the midpoints of the opposite faces of the lattice pass throughan origin M, which is the measurement point, and form X, Y and Z axes ofthe cubic lattice 64. The lines between the microphones form diagonals(not shown) across the faces of the cubic lattice, which also representthe edges of the regular tetrahedron and pass through the midpoints 12,13, 14, 23, 24 and 34 with a length of dimension d. These lines formhypotenuse lines for the respective faces of the cubic lattice 64 sothat the edges of the sides of the lattice have dimension d/√{squareroot over (2)}.

In FIGS. 3, 4 and 5, numeral 40 generally indicates an acoustic vectorprobe formed in accordance with the invention. Probe 40 includes afixture 42 being an annular member formed as a ring with a centralopening 46. Protruding from the ring are four support tubes for themicrophones parallel to the axis of the ring, two on one side of thering pointing in one direction and two on the reverse side pointing inthe opposite direction. These tubes are spaced around the ring at ninetydegree intervals at openings in the ring at 48, 50, 52 and 54, andcentered on an annular centerline 56 having a diameter d. The pair oftubes 58 on one side of the ring is attached to the ring coincident withdiametrically opposite openings 48 and 50, and the pair of tubes 60 onthe reverse side of the ring is attached to the ring coincident withdiametrically opposite openings 52 and 54. The outer ends of the supporttubes 58, 60 are each a distance d/(2√{square root over (2)}) from thecentral base plane 64 of the ring and a distance d/√{square root over(2)} from each other. Within the ends of the two support tubes 58 arelocated microphones 1, 2 and within the ends of the support tubes 60 arelocated microphones 3 and 4.

The four microphones are substantially identical and include soundadmitting orifices 62 which are located with their upper surfaces flushwith the ends of the tubes 58 in the case of the microphones 1, 2 andflush with the ends of tubes 60 in the case of microphones 3, 4. Themicrophones are preferably small electret microphones such as the FGseries available from Knowles Electronics LLC, of Ithaca Ill., or the EMseries of Primo Microphones Inc., of McKinney, Tex. The Knowlesmicrophones are very small having outer diameters of less than 2.6 mmwith similar body lengths, while the Primo EM microphones typically havean outside diameter of about 5.8 mm. Despite their small size theKnowles FG microphones have a sensitivity comparable to largermicrophones. The smallness of these microphones makes it possible tolocate their centers of sensitivity more precisely and hence todetermine the separation distance d more exactly.

For the finite difference approximations in the measurement calculationsto be valid, the microphone spacing d has to be smaller than theshortest wavelength (corresponding to the highest frequency f) beingmeasured, satisfying the condition kd/2<1, where kc=2nf, k being thewave number, c the speed of sound in air (about 344 m/s) and f the upperfrequency limit. For example, if the instrument is designed for an upperfrequency limit of 5 kHz, which is typical of most machinery noise, thecorresponding wave number k is about 0.0913. Hence d has to less thanabout 20 mm. Suppose d is 15 mm. The two microphones then protrude fromthe central base plane of the ring a distance d/(2√{square root over(2)}), which is about 5.30 mm.

It is seen from FIGS. 3, 4 and 5 that the Knowles FG series electretmicrophones readily fit into this configuration, as do other microphonessuch as the Primo EM series. Because of the smallness of the preferredKnowles microphones, it is possible to make the separation distance dmuch less than 15 mm, thus permitting measurements to be made atfrequencies up to about 15 kHz. For larger microphones, particularly ofthe condenser type, it would not be possible to attain this high afrequency. In principle, of course, there is no reason that condensermicrophones could not be used. The structure for holding the microphonescould be different from that in FIGS. 3, 4 and 5, provided the locationsof the microphones continues to correspond to those shown in FIG. 2. Theadvantages of the structure in FIGS. 3, 4 and 5 are: (a) the microphonesare symmetric on the two sides of the base ring so that they detectsound equally from both directions; (b) the measurement point M is welldefined; (c) the procedure for normalizing and calibrating can beapplied easily. Since the dimensions of the probe are required to bemuch less than the wavelengths being measured, the effect of diffractionwill be insignificant.

FIGS. 6 and 7 depict an apparatus for normalizing and calibrating thevector probe whose use will be explained in the next section.

FIGS. 8 and 9 illustrate how the frequency range of the measurements canbe extended by using a pair of nested vector probes with the sameorientation and measurement point. As will be explained later thesmaller inner probe extends the accuracy of the measurements to higherfrequencies and the larger outer probe to lower frequencies. The twosets of measurements are performed simultaneously and are merged in thesignal processor to cover the combined frequency range.

FIG. 10 shows how the X, Y, Z components of the sound-intensity vectorare expressed in terms of azimuth and elevation to indicate thedirection of a sound source. This is discussed more fully later.

FIG. 11 shows a holder for the vector probe that can be adjusted inazimuth and elevation. The direction of a noise source is indicated bylaser pointers. The narrow leads (not shown) from each microphone arerouted along the spokes of the holder and around the holder's outerframe to the handle, proceeding then to the analog-to-digital converterand the digital signal processor. The handle can contain batteries forthe laser pointers in the holder.

Normalization and Calibration of the Microphones in the Probe

To measure acoustic intensity accurately, the acoustic sensitivity ofthe array of four microphones in the probe has to be omnidirectional,i.e. equally sensitive to sound from any direction. Because of theirsmall size relative to the acoustic wavelength, the sensitivities of theelectret microphones in the probe are individually omnidirectional.However, if the sensitivity of the tetrahedral arrangement in the probeis to be omnidirectional, the constituent microphones have to respondidentically. In the normalization procedure described here, themicrophones are made to respond identically in the digital signalprocessor by determining the transfer function between each microphoneand a standard calibration microphone. The procedure also calibrates themicrophones. This procedure is designed for use with the probe in thefield.

Presently microphones are calibrated in the field with a hand-heldcalibrator only at a single frequency. More complete calibration has tobe performed at a special laboratory away from the test site, usingprocedures that are considered beyond the capabilities of a typical testengineer. Such procedures are described, for example, in

-   11. V. NedzeInitsky, 1997, “Calibration of Pressure and Pressure    Gradient Microphones.”, Vol. 4, Chap. 157, Encyclopedia of    Acoustics, edited by M. J. Crocker, John Wiley & Sons, Inc., New    York.

In the invention, normalization and calibration of the vector probe isperformed with the closed-chamber apparatus 72, shown in FIG. 6. Acondenser microphone C, such as the Bruel & Kjaer quarter-inch model4136 or eighth-inch model 4138, is used as a standard comparisonmicrophone for normalization and calibration of the microphones in theprobe. The procedure is performed using the fixture 76 shown in FIG. 7,inserted into one end of the calibration tube 80, with the loudspeaker82 at the other end, emitting pseudo-random white noise or otherbroadband time-invariant or stationary signals.

The fixture 76 in FIG. 7 places the standard microphone C in the sameplane as microphones 1 and 2 of the probe supported by the two tubes 58.Signals received simultaneously at the microphone 1 and the calibrationmicrophone C, denoted respectively by p1(t) and pC(t) in the timedomain, are recorded by the signal processor 38 and transformed into thefrequency domain using discrete Fourier transforms (DFTs) indicated bythe italic prefix F. DFT techniques are described in texts such as,

-   12. W. H. Press, S. A. Tuekolsky, W. T. Vetterling and B. P.    Flannery, 1996, “Numerical Recipes In C++: The Art of Scientific    Computing”, Cambridge University Press, Cambridge, UK.

The complete normalization and calibration procedure can be bestdescribed as follows. Standard DFT techniques are performed to determinethe transfer function H1C(f) between microphone 1 and the calibrationmicrophone C, as followsH1C(f)=G1C(f)/G11(f)  (1)where G1C(f) is the cross-spectrum between the signal at microphone 1and the calibration microphone C, given byG1C(f)=FpC(f).Fp1(f)*  (2)and G11(f) is the auto-spectrum of the signal at microphone 1 given byG11(f)=Fp1(f).Fp1(f)*  (3)where the asterisks denote the complex conjugate. To make the signalFp1(f) at microphone 1 look like the signal FpC(f) at the calibrationmicrophone C, it is multiplied by the transfer function in Equation (1)to giveFp1C(f)=Fp1(f).H1C(f)  (4)The process is repeated for microphone 2 using relations correspondingto Equations (1) through (4), specificallyH2C(f)=G2C(f)/G22(f)  (5)whereG2C(f)=FpC(f).Fp2(f)  (6)andG22(f)=Fp2(f).Fp2(f)  (7)To make Fp2(f) look like FpC(f), Fp2(f) is multiplied by the transferfunction in Equation (5) to giveFp2C(f)=Fp2(f).H2C(f)  (8)

Transfer functions for microphones 3 and 4 are obtained in the same wayby reversing the vector probe so that the tubes 60 are inserted into thefixture 76 placing microphones 3 and 4 in the same plane as thecalibration microphone C. In this way all four microphones in the probecan be made to look like the calibration microphone C, making thesensitivity of the probe omnidirectional and also calibrating theindividual microphones. The transfer functions are stored in the signalprocessor for later use in measurements with the probe.

Different types and sizes of the fixture 76 can be used for differentsizes of probes, particularly for the nested probes shown in FIGS. 8 and9 and for the probe holder in FIG. 11.

Measurement Calculation

Calculations to determine the components of the sound-intensity vectorat a point in space, from measurements at the four microphones in thevector probe, are performed in the signal processor. The calculationsalso determine the other two basic quantities of acoustics, namely soundvelocity and sound pressure, at the same measurement point. Thecalculation method is best described as follows.

At the microphones 1, 2, 3 and 4 at the vertices of the regulartetrahedron in FIG. 2, the corresponding sound pressures p1, p2, p3 andp4 are measured and digitized. To ensure omnidirectionality and accuracythe discrete Fourier transforms (DFTs) of the sound pressures are thencomputed, normalized and calibrated using the transfer-functionprocedure described in the previous section, giving the modifiedtransforms Fp1(f), Fp2(f), Fp3(f) and Fp4(f). For simplicity, thefrequency dependence (f) will be dropped. Finite differenceapproximations (derived from Taylor series expansions) are then appliedto obtain the DFTs of the sound pressures at the six midpoints of theedges of the regular tetrahedron at 12, 13, 14, 23, 24 and 34 in FIG. 2,giving respectively

$\begin{matrix}\begin{matrix}{{Fp12} = {\left( {{Fp1} + {Fp2}} \right)/2}} \\{{Fp13} = {\left( {{Fp1} + {Fp3}} \right)/2}} \\{{Fp14} = {\left( {{Fp1} + {Fp4}} \right)/2}} \\{{Fp23} = {\left( {{Fp2} + {Fp3}} \right)/2}} \\{{Fp24} = {\left( {{Fp2} + {Fp4}} \right)/2}} \\{{Fp34} = {\left( {{Fp3} + {Fp4}} \right)/2.}}\end{matrix} & (9)\end{matrix}$These approximations are accurate to the second order, i.e. order(kd)²/4, provided.kd/2<1  (10)

The components of the sound-intensity vector at the measurement point Mare determined from the sound pressure DFTs in Equation (9), using thecross-spectral formulation described by Fahy, Chung and Hickling et al.The components areFIX=−Im CS[Fp24, Fp13]/(ρ2πf(d/√{square root over (2)}))FIY=−Im CS[Fp23, Fp14]/(ρ2πf(d/√{square root over (2)}))FIZ=−Im CS[Fp12, Fp34]/(ρ2πf(d/√{square root over (2)}))  (11)where Im is the imaginary part and CS is the cross spectrum of the soundpressures at the midpoints of the opposite edges of the imaginaryregular tetrahedron in FIG. 2, and p is the density of the fluid medium,which is approximately 1.2 kg/m ³ for air. The amplitude is given byFIA=√[FIX ² +FIY ² +FIZ ²]  (12)Sound intensity is expressed in SI units of watts per meter squared persecond.

The classical far field approximation for sound intensity is stillwidely used and may be employed in the computation as a comparison. Thisapproximation is valid for plane and spherical waves and gives thesound-intensity amplitude asFTAff=|FpM| ²/(ρc)  (13)where c is the speed of sound in the fluid medium (approximately 344 m/sfor air) and FpM is the finite-difference approximation of the DFT ofthe sound pressure at the measurement point M given byFpM=(Fp1+Fp2+Fp3+Fp4)/4  (14)in SI units of pascals per hertz.

The components of the sound-velocity vector are obtained from thefinite-difference approximations of the X, Y and Z components of thepressure gradient at the measurement point M, which areFDpX=(Fp24−Fp13)/(d/√{square root over (2)})FDpY=(Fp23−Fp14)/(d/√{square root over (2)})FDpZ=(Fp12−Fp34)/(d/√{square root over (2)})  (15)where again these are accurate to second order. The X, Y and Zcomponents of the DFTs of the sound-velocity vector are thenFVX=K FDpXFVY=K FDpYFVZ=K FDpZ  (16)where the coefficient K=i/(p2πf), i being the square root of −1. In SIunits these components are in meters per second per hertz. The amplitudeof each component is given byFVXA=|FVX|, FVYA=|FVY| and FVZA=|FVZ|.The amplitude of the sound velocity vector is then given byFVA=√{square root over (()}FVXA ² +FVYA ² +FVZA ²)  (17)Unlike the sound-intensity vector, the sound-velocity vector has a 180degree ambiguity in direction.

The above equations can be developed using software such as LABVIEW andMATLAB and converted into C++ or other suitable computer language foruse in the signal processor.

Extending the Frequency Range of the Measurements by Combining two ormore Tetrahedral Arrangements of Microphones

The vector probe has two limitations in the frequency range, one at highfrequencies and the other at low frequencies. At high frequencies it isnecessary to satisfy the condition in Equation (10) to preserve theaccuracy of the finite difference approximations. Hence, to extend thefrequency range as high as possible, the spacing d between themicrophones must be as small as possible. However if the microphones aretoo close, error is introduced at low frequencies due to taking thedifference between almost equal quantities, as in Equation (15). Thiserror can be reduced only by increasing the microphone spacing d.Clearly it is not possible both to increase and decrease the spacing dfor measurements at the same point. To extend the frequency range atboth high and low frequencies, it is necessary to have at least twotetrahedral arrangements, one for the upper end of the frequency scaleand the other for the lower end.

FIGS. 8 and 9 show a nested set 90 of two acoustic probes 92, 94arranged for this purpose. The probes are similar to those shown inFIGS. 3 and 4 but differ in size, specifically in the dimension d, tocover the upper and lower parts of the frequency range. The probes 92,94 are nested one inside the other with the same orientation andmeasurement point M, and measurements are made simultaneously at bothprobes. To cover a desired frequency range, it may be necessary to havemore than two probes in the nested set. Correspondingly the number ofinput channels to the digital signal processor has to be increased toequal the number of microphones in the nested set. Also calculation inthe digital signal processor ensures that measurements in differentparts of the frequency range merge appropriately with each other.

Using the Vector Probe to Determine the Direction of a Sound Source inAir

The acoustic vector probe determines the three components of the soundintensity vector at the measurement point M internal to the probe. Thisinformation can then be used to find the direction of a sound source,assuming that sound propagates in a straight line from the source to themeasurement point. The direction of a sound source can be determined interms of the horizontal (azimuth) angle θ.and the vertical (elevation)angle φ. The combination of these two angles specifies the direction ofthe source, as shown in FIG. 10. Other angles could be used, but azimuthand elevation are commonly used and easily understood. The vector probecan point horizontally in the direction of the Z-axis while the Y-axisis vertical as shown in FIG. 2. The angles θ and φ are determined fromthe relationsθ=arccos(FIZ/FIXZ)  (18)andφ=arcsin(FIY/FIA)  (19)where FIXZ=√[FIX²+FIZ²] and the other terms come from Equations (15) and(16). The angles θ and φ are functions of frequency. They can berepresented over the frequency range by a set of discrete points in anelevation-azimuth (or vertical-horizontal) plot on a monitor screen,relative to the direction of the probe, as in Hickling et al. In freespace the points will generally coincide. Tests in an anechoic chambercan then be used to check the omnidirectionality and accuracy of theprobe. However in practice there will be a scatter of the points due tothe acoustic environment. Color-coding of the points on the monitorscreen can show the frequency dependence of the scatter. Color-coding isa new idea that was not used by Hickling et al, but it can be a richsource of information. The components of the velocity vector can be usedto determine direction in a similar way, except that there is a180-degree ambiguity in the data.

The assumption that sound propagates in a straight line from the sourceto the probe is not always valid, because conditions such as temperatureand turbulence in the acoustical medium may affect the transmissionpath. Corrections can be made. However, we will restrict ourselves tothe straight-line assumption. In addition to being used in architecturalacoustics and noise control, the direction-finding capabilities of avector probe could provide a model for the directional hearing ofanimals.

An example of a device for determining direction is shown in FIG. 11.Here a vector probe 40 is shown contained in a holder 96 which can beadjusted in azimuth 98 and elevation 100. The device can be hand-heldand includes laser pointers 102 to show the direction of a noise source.A human operator can adjust the holder in the direction indicated by theprocessor. The laser pointers then point to the source. It would bepossible also to locate the holder remotely and to operate it with acomputer controller. The fixture shown in FIG. 7 can be adapted so thatthe probe can be normalized and calibrated without having to be removedfrom the holder.

FIG. 11 indicates that the leads from the microphones can be routedalong the spokes 104 and around the outer frame of the holder to thesignal processor. It also indicates that the laser pointers can bepowered by batteries in the handle 106 of the holder.

While the invention has been described by reference to certain preferredembodiments, it should be understood that numerous changes could be madewithin the spirit and scope of the inventive concepts described.Accordingly it is intended that the invention not be limited to thedisclosed embodiments, but that it have the full scope permitted by thelanguage of the following claims.

1. Acoustic measurement apparatus comprising: an omnidirectionalacoustic vector probe including four small microphones supported by aspace frame at the vertices of an imaginary regular tetrahedron; a firstpair of said microphones facing a same first direction a second pair ofsaid microphones in a backward-facing relationship with said first pairand facing a same opposite direction; said microphones connected to ananalog digital converter for conversion of analog signals to digitalform; said converter connected to a digital signal processor programmedto normalize and calibrate the signals and to compute sound intensity,velocity and pressure at a measurement point in space; and saidprocessor connected to an output apparatus for outputting themeasurement results of the computations.
 2. The invention as in claim 1wherein the processor is additionally programmed to compute thedirection of a sound source from the direction of the sound-intensityvector.
 3. The invention as in claim 2 wherein the direction of a soundsource is displayed on a computer screen as a plot in a grid relative toa coordinate system of the vector probe.
 4. The invention as in claim 3wherein frequency dependence of points plotted in the grid on thecomputer screen is illustrated by color-coding.
 5. The invention as inclaim 1 where said microphones have maximum dimensions less than 6 mm.6. The invention as in claim 1 including at least one input channel foreach of the microphones in the acoustic measurement apparatus.
 7. Aprecisely constructed acoustic vector probe comprising: a space framesupporting four substantially identical microphones, at the vertices ofan imaginary regular tetrahedron, each microphone spaced the samedistance d from the other microphones, a first pair of the microphonesfacing a same first direction and lying in a plane separated by adistance d/√{square root over (2)} from a parallel plane containing asecond pair of the microphones, in a back-to-back relationship with saidfirst pair and facing a same opposite direction from said firstdirection and defining a set of Cartesian axes formed by lines joiningthe midpoints of opposite edges of the tetrahedron whose center is themeasurement point of the probe, the space frame including a supportingmember lying midway between the said planes and having spaced openingswith microphone support means extending from the openings.
 8. Aprecisely constructed acoustic vector probe comprising: a space framesupporting four substantially identical microphones, at the vertices ofan imaginary regular tetrahedron, each microphone spaced the samedistance d from the other microphones, two of the microphones lying in aplane separated by a distance d/√{square root over (2)} from a parallelplane containing the other two microphones and defining a set ofCartesian axes formed by lines joining the midpoints of opposite edgesof the tetrahedron whose center is the measurement point of the probe,the space frame including a supporting member lying midway between thesaid planes and having spaced openings with microphone support meansextending from the openings; and wherein said support means includestubes extending normal to said member and supporting said pairs ofmicrophones, one pair lying on one side of said member facing in onedirection and the other pair on the reverse side facing in the oppositedirection.
 9. The invention as in claim 8 wherein said member is a ringhaving one pair of said microphones and said tubes spaced from the othersaid pair of microphones, alternating equally on a diameter of dimensiond, said tubes extending normal to a mid base plane of the ring adistance d/(√{square root over (2)}), the center of said mid base planebeing the measurement point of the probe.
 10. A precisely constructedacoustic vector probe comprising: a space frame supporting foursubstantially identical microphones, at the vertices of an imaginaryregular tetrahedron, each microphone spaced the same distance d from theother microphones, two of the microphones lying in a plane separated bya distance d/√{square root over (2)} from a parallel plane containingthe other two microphones and defining a set of Cartesian axes formed bylines joining the midpoints of opposite edges of the tetrahedron whosecenter is the measurement point of the probe, the space frame includinga supporting member lying midway between the said planes and havingspaced openings with microphone support means extending from theopenings; and where the vector probe is contained in a holder which canbe adjusted so that the probe points in the direction of a sound sourceand the direction of the source can be indicated by laser pointers orother means.
 11. The invention as in claim 10 where the said holder canbe adjusted by hand or controlled by a digital controller.